Question

multiplying decimals
part 1: convert to fractions — solve the problems below by converting the factors to fractions. convert the product back into a decimal. be sure to show your work.

1. $0.03 \times 0.4$
2. $0.06 \times 2$
3. $0.009 \times 5$
4. $0.3 \times 3$
5. $0.001 \times 25$

part 2: the standard algorithm — solve the problems below using the standard algorithm. be sure to show your work.

1. $2.5 \times 6$
2. $2.05 \times 6$
3. $0.33 \times 0.33$
4. $5.8 \times 9.3$
5. $0.58 \times 0.93$

Explanation:

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Part 1: Convert to Fractions

Problem 1: $0.03 \times 0.4$

Step1: Convert decimals to fractions

$0.03 = \frac{3}{100}$, $0.4 = \frac{4}{10}$

Step2: Multiply the fractions

$\frac{3}{100} \times \frac{4}{10} = \frac{12}{1000}$

Step3: Convert to decimal

$\frac{12}{1000} = 0.012$

Problem 2: $0.06 \times 2$

Step1: Convert decimal to fraction

$0.06 = \frac{6}{100}$, $2 = \frac{2}{1}$

Step2: Multiply the fractions

$\frac{6}{100} \times \frac{2}{1} = \frac{12}{100}$

Step3: Convert to decimal

$\frac{12}{100} = 0.12$

Problem 3: $0.009 \times 5$

Step1: Convert decimal to fraction

$0.009 = \frac{9}{1000}$, $5 = \frac{5}{1}$

Step2: Multiply the fractions

$\frac{9}{1000} \times \frac{5}{1} = \frac{45}{1000}$

Step3: Convert to decimal

$\frac{45}{1000} = 0.045$

Problem 4: $0.3 \times 3$

Step1: Convert decimal to fraction

$0.3 = \frac{3}{10}$, $3 = \frac{3}{1}$

Step2: Multiply the fractions

$\frac{3}{10} \times \frac{3}{1} = \frac{9}{10}$

Step3: Convert to decimal

$\frac{9}{10} = 0.9$

Problem 5: $0.001 \times 25$

Step1: Convert decimal to fraction

$0.001 = \frac{1}{1000}$, $25 = \frac{25}{1}$

Step2: Multiply the fractions

$\frac{1}{1000} \times \frac{25}{1} = \frac{25}{1000}$

Step3: Convert to decimal

$\frac{25}{1000} = 0.025$

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Part 2: Standard Algorithm

Problem 1: $2.5 \times 6$

Step1: Multiply as whole numbers

$25 \times 6 = 150$

Step2: Place decimal point

1 decimal place total: $15.0 = 15$

Problem 2: $2.05 \times 6$

Step1: Multiply as whole numbers

$205 \times 6 = 1230$

Step2: Place decimal point

2 decimal places total: $12.30 = 12.3$

Problem 3: $0.33 \times 0.33$

Step1: Multiply as whole numbers

$33 \times 33 = 1089$

Step2: Place decimal point

4 decimal places total: $0.1089$

Problem 4: $5.8 \times 9.3$

Step1: Multiply as whole numbers

$58 \times 93 = 5394$

Step2: Place decimal point

2 decimal places total: $53.94$

Problem 5: $0.58 \times 0.93$

Step1: Multiply as whole numbers

$58 \times 93 = 5394$

Step2: Place decimal point

4 decimal places total: $0.5394$

Answer:

Part 1:

1. 0.012
2. 0.12
3. 0.045
4. 0.9
5. 0.025

Part 2:

1. 15
2. 12.3
3. 0.1089
4. 53.94
5. 0.5394